The Hatter, the Hare, the Rabbit, the Mouse, Alice and I met for a Tea Party. The table had two sides, with three chairs on each side, numbered like so:
Side A: 1 2 3
Side B: 6 5 4
Chair one was across from chair 6, chair 2 across from chair 5, etc. We would sit down one at a time, in any chair we choose. The first guest to sit down was called the first guest. After the second guest sat down, however, everyone moved clockwise to the next chair. This behavior was continued after the fourth and sixth guest sat down.
My question is, after everyone had been seated, where was I seated?
(1) The first guest sat in chair 1.
(2) The mouse sat down last.
(3) After the first time everyone moved, no one had been on side B yet.
(4) The Hatter and Alice choose the same starting chair.
(5) When I was in chair 1, the Rabbit was in chair 6.
(6) I started on side B, but didn't end there.
(7) The hare moved all three times.
(8) Alice ended up between the mouse and the hare.
(9) I sat down after the rabbit but before the hatter.
(10) The mouse sat down in an odd numbered chair.
Also, a bonus question. Who am I?
Guest 1 starts in Chair 1 (Clue 1). After Round 2, nobody is in Seats 4,5 or 6. (Clue 3). At the start of Round 2, Guest 1 is in chair 1, so Guest 2 can't sit there. Guest 2, can't sit in chair 3, as they would move to chair 4 at the end of round 2, in violation of clue 3. Therefor, Guest 2 sits in Chair 2.
Guests 1 and 2 are the only ones who move 3 times. Thus the hare is Guest 1 or Guest 2. (Clue 7). Guest 1 finishes in Chair 4 after 3 moves, and Guest 2 finishes in Chair 5. The mouse moves only once, and sits in an odd chair.(Clues 2,10) The mouse can't sit in Chair 3, as Guest 1 is sitting there after Round 5. So the mouse sits in Chair 1 or Chair 5, and ends up in Chair 2 or Chair 6. Alice is between the mouse and the hare.(Clue 8). The hare is either 4 or 5, which follows from the hare being Guest 1 or Guest 2. If in chair 5, the mouse can't be in Chair 6, because Alice is between the mouse and the hare.(Clue 8). Thus, the mouse would be in chair 2. However, Alice could not then be between the mouse and hare. So, the hare in is Chair 4 and is Guest 1.
I sat down after the Rabbit but before the Hatter(Clue 9). Since the Hare is Guest 1, the Rabbit can only be guest 2 or guest 3. Rabbit cannot be guest 4, as the Rabbit is followed by me, Hatter and Mouse. (Clues 9, 2). However, the Rabbit sat in Seat 6. Guest 2 never sat in seat 6, as that guest started in 2 and finished in 5. Thus the Rabbit is Guest 3. I am Guest 4. The Hatter is Guest 5. This means that Alice is Guest 2. Since Guest 2 started at Chair 2, the Hatter also started at Chair 2 (Clue 4). Since the Hatter is Guest 5, the Hatter ended up in Chair 3. As Guest 2 moves 3 times, Alice ends up in Chair 5.Since the Hare is in Chair 4, and Alice in Chair 5, the mouse starts in Chair 5 and ends up in Chair 6. (Clue 8).
I started on Side B, but finished on Side A. (Clue 6). As I am Guest 4, I move twice, so I start in either Seat 5 or Seat 6. Since the Rabbit is in Seat 6 when I am in Seat 1 (Clue 5), and the Rabbit also moves only twice, the Rabbit starts in Seat 4 or Seat 5. However, if the Rabbit started in Seat 4, the Rabbit would finish in Seat 6, which is impossible, as we have already determined that the mouse finishes in Seat 6. So, the Rabbit starts in Seat 5, finishes in Seat 1. I start in Seat 6 and finish in Seat 2.
Summary:
Guest 1 -- Hare--Starts Seat 1--Ends Seat 4
Guest 2 -- Alice--Starts Seat 2--Ends Seat 5
Guest 3--Rabbit--Starts Seat 5--Ends Seat 1
Guest 4--I--Starts Seat 6--Ends Seat 2
Guest 5--Hatter--Starts Seat 2--Ends Seat 3
Guest 6--Mouse--Starts Seat 5--Ends Seat 6.
Solution
